Here is the full list of all 40 The Forgotten City achievements. It takes around 12-15 hours to unlock all of the achievements on Windows.
Reach the best ending with the smallest number of loops
Talk your way through every possible confrontation
Help Galerius romance Equitia
Lie 10 times
Finish the game without looping through time once
Topple 10 peeled statues by kicking others into them
Die from hornet stings
Allow Fabia to die in the collapsing temple
Skip the city tour
Free the captive and shoot her captor with your gun
Loop through time ten times
Trigger The Golden Rule by stealing 5 times
Reach Ending 3 of 4
Reach Ending 2 of 4
Use Photo Mode
Reach Ending 4 of 4
Assemble as many people as possible in the Museum
Intimidate the creator of The Golden Rule
Confront the creator of The Golden Rule
Reach Ending 1 of 4
Save Ulpius's life
Have Duli released from his cell
Find all three missing persons
Enter the upper cistern in an unconventional way
Find treasure using the golden bow
Survive the Palace
Gild your first thing
Dodge 3 boulders
Discover Underworld icons Sisyphus, Tantalus, Ixion and the Belide
Learn the true identity of the stranger by the river
Solve Vergil's problem
Read 10 different grafitti
Steal 2000 coins after the Golden Rule is broken
Get rejected by Aurelia
Save Iulia's life
Discover what lies beneath the city
Save Fabia's life
Enter a villa with a daring leap
Pick up the sponge on a stick
Loop through time once